2. Click when ready...

3. Individual Competition Part II Questions 26 - 50

4. There are 25 multiple choice questions You have 2 minutes to finish each question There will be no break in this round A trial question will now follow Click when ready...

5. You now have 30 seconds left 10987654321STOP Trial Question (2 minutes) (a)– log 2 5 (b) log 5 2 (c) log 10 5 (d) log 2 5 (e) If 3 = k. 2 r and 15 = k. 4 r, then r =

7. You now have 30 seconds left 10987654321STOP Suppose that * is an operation on the integers defined by a*b = a 2 +b. What is the value of 3 * (2 * 1)? (a) 12 (b) 14 (c) 54 (d) 170 (e) 172 26

8. You now have 30 seconds left 10987654321STOP 27.An office building has 50 storeys, 25 of which are painted black and the other 25 of which are painted gold. If the number of gold storeys in the top half of the building is added to the number of black storeys in the bottom half of the building, the sum is 28. How many gold storeys are there in the top half of the building? A.3 B. 14 C. 22 D. 24 E. None of these

9. You now have 30 seconds left 10987654321STOP 28. What is the number of distinct real numbers r which have the property that the median of the five numbers r,6,4,1,9 is equal to their mean? A. 0 B. 1 C. 2 D. 3 E. 5

10. You now have 30 seconds left 10987654321STOP Two perpendicular line segments divide a large rectangle into 4 small rectangles. The areas of 3 of these 4 small rectangles are shown. What is the area of the other small rectangle? 6 9 8 (a) 12 (b) 13 (c) 14 (d) 15 (e) 16 29

11. You now have 30 seconds left 10987654321STOP 30.A can build a building in 3 hours, B can build the building in 4 hours. Together, A and B, and C can build the building in 1 hour. D can build the building in half the time it takes C to build the building. How long does it take C and D to build the building together? A. 36 minutes B. 48 minutes C. 60 minutes D. 72 minutes E. 84 minutes

12. You now have 30 seconds left 10987654321STOP 31.Triangle ABC has sides AB = 12, BC = 10, and AC = 20. A circle is drawn with radius 10 centered at C. Segment AB is extended, intersecting the circle at point D. Determine the length of BD. A.2√21 B. 10 C. 2√39 D. 13 E. None of these

13. You now have 30 seconds left 10987654321STOP 32.A block of wood in the form of a cuboid 6" x 9" x 14" has all its six faces painted pink. If the wooden block is cut into 756 cubes of 1" x 1" x 1", how many of these would have pink paint on them? A.420 B.560 C. 585 D. 624 E. 758

14. You now have 30 seconds left 10987654321STOP 33. If x + y = 0 and x ≠ 0, then what is the value of x 2007 y 2007 ? (a) -2007 (b) -1 (c) 0 (d) 1 (e) 2007

15. You now have 30 seconds left 10987654321STOP 34. The perimeter of a rectangle is P, and the area of the rectangle is A. What is the product of the diagonals? A. B. C. P 2 – 2A D. P 2 + 2AE. None of these

16. You now have 30 seconds left 10987654321STOP 35.

17. You now have 30 seconds left 10987654321STOP 36.

18. You now have 30 seconds left 10987654321STOP 37. Evaluate the sum 1- 2 + 3 – 4 + 5 – 6 +…+ 997 – 998 + 999 - 1000 A. -500B. -1000 C. -999D. -1001 E. 500500

19. You now have 30 seconds left 10987654321STOP 38. Let N be the largest integer for which both N and 7N have exactly 100 digits each. What is the 50 th digit (from the left) of N? A.5D. 4 B. 1E. 2 C. 8

20. You now have 30 seconds left 10987654321STOP 39.

21. You now have 30 seconds left 10987654321STOP 40.The number 6 is divisible by 1, 2, 3 and 6, so 6 has 4 divisors. How many divisors has 6718464 = (2^10) x (3^8)? A. 99B. 109C. 98D. 100E.93 (Remark. “a^b” means “a to the power of b”.)

22. You now have 30 seconds left 10987654321STOP 41.

23. You now have 30 seconds left 10987654321STOP 42.A cylindrical beaker 8 cm high and 12cm in circumference was standing on a table. On the inside of the beaker, 2 cm from the top, is a drop of honey. Diametrically opposite the honey and lower is a spider which is on the outside of the beaker, 2 cm from the bottom. What is the shortest distance the spider has to walk to reach the honey? A. 10 cm B. 12 cm C. 13 cm D. 100 cm E. None of the above

24. You now have 30 seconds left 10987654321STOP 43.

25. You now have 30 seconds left 10987654321STOP 44. In year N, the 300th day of the year is a Tuesday. In year N + 1, the 200th day is also a Tuesday. On what day of the week did the 100th day of the year N-1 occur? A.Thursday B.Friday C.Saturday D.Sunday E.Monday

26. You now have 30 seconds left 10987654321STOP 45. A square with sides of length 1 is divided into two congruent trapezoids and a pentagon, which have equal areas, by joining the centre of the square with points on three of the sided, as shown. Find r, the length of the longer parallel side of each trapezoid. A. B. C. D. E. r

27. You now have 30 seconds left 10987654321STOP 46.

28. You now have 30 seconds left 10987654321STOP 47. In square ABCD, with sides of length 2, segments AE, BF, CG, and DH are drawn (figure below), bisecting the sides. These segments form quadrilateral JKLM. Determine the area of quadrilateral JKLM. A.2/5 B.4/5 C.1 D.2 E.None of these A 1 H 1 B D F C E G L K J M

29. You now have 30 seconds left 10987654321STOP 48. Define a sequence of real numbers by and for all Then equals A.33 33 B.33 99 C.99 33 D.99 99 E.None of these

30. You now have 30 seconds left 10987654321STOP 49.The equiangular convex hexagon ABCDEF has AB = 1, BC = 4, CD = 2 and DE = 4. The area of the hexagon is A. B. C. 16 D. E.

31. You now have 30 seconds left 10987654321STOP 50.